Your model is simple, nice, but wrong. Experimentally proven wrong by the fact that developed nations (where food is not an issue for most of the population) there are declining birth rates.

But the developed nations didn't become developed simply by throwing food at them. In fact, one could argue that space programs were a significant factor in their development, and therefore prevented more starvation than food aid ever did.

I think you need to take that ecology class again. Humans are bit different than tadpoles; I'm being serious there is more complexity at work than "more food --> more offspring." Your basic ecology simpleton logic doesn't include any conception of sociological factors that are inherent in human populations. Does your basic ecology conceive of frogs deciding to either delay or even not engage in reproduction in favor of careers?

I believe there's more of an inverse correlation: the wealthier a population, the lower its birth rate. One-off starvation events caused by unusual weather in agricultural societies are one thing, where temporary aid would be helpful. But poverty in particular places isn't caused by a global shortage of food, but local factors such as incompetent and/or corrupt administration or culture and subsequent lack of economic development. There may not be much that a US organization could do about it.